Question: What is $35_8-74_8?$ Express your answer in base 8.
Explanation: When we are subtracting, we want to subtract a smaller number from a bigger number. We can pull out a negative sign in order to accomplish this:  \[ 35_8-74_8 = -(74_8 - 35_8). \]Now, we can line in the numbers and subtract just as we do in base 10.  For example, when we borrow from the $8^1$s place, the digit 1 in the units place becomes $4+8=12$, while the digit in the $8^1$s place decreases by 1. Continuing in this way, we find $$\begin{array}{c@{}c@{}c@{}c}
& & \cancelto{6}{7} & \cancelto{12}{4}_8 \\
& - & 3 & 5_8 \\
\cline{2-4}
& & 3 & 7_8 \\
\end{array}$$Therefore, $35_8-74_8 = -(74_8 - 35_8) = \boxed{-37_8}$.